TOPIC:

Hi, a couple of things to look at -

1. All of your compressions look pretty low to me given that the manufacturer info you posted is 120 - 190 psi (the lower the compression is, the faster you need to spin the motor to get it to start - It is not uncommon to tow start older cars with worn motors for this very reason ) have you checked valve clearances ?
2. 10.75v during cranking is fine, anything above 10v is OK
3. Bench testing the starter will give a meaningless result as there is no load on it
4. When checking for resistance faults in wiring the most accurate method is to measure voltage drop not ohms (see my electrical fault finding guide in FAQ section of forum index which explains how and why)
5. If the starter is noisy in operation are you sure the starter clutch isn't at fault, this slipping would also stop it starting

Latest update --  I bench tested the starter and it ran smooth, not much voltage drop out the bike as there was no load on it, at least I know it runs fairly smooth indicating the bearings are decent, etc. Started unhooking accessory connections that aren't needed for the engine to crank and start. After unhooking the "Reserve Lighting Device" and giving it a try it started right up and surprised the heck out me, sort of rough running at first then smoothed out bit, carbs of course still need adjusting. Ran it for about 3 minutes and shut it off. Did a restart and it started right up. Thinking that must have been the problem, plugged the device back in and it started right up, ran it for a while shut it off to scratch my head, how in the world would it start if that was the problem. Tried to start it again, crank, crank, nothing, unplugged it again, still won't start. Went through more wiring, trying to find some sort of rubbed through wire, nothing. jiggled wires at the coils, and plugs. Tried to start it after some more troubleshooting, started right up and ran for a while sputtered and died. So in short making progress, I now know it's some sort of electrical gremlin that I can't seem to find. Throughout working on it this morning I was able to get to start and run four different times. It's weird when it starts, it almost fires off instantly like one would expect. One of the times it started after about 10 seconds of steady cranking. I hate abusing the starter and making it crank for extended periods of time. I think I unplugged everything that is associated with it being able to start, and just cannot get to the bottom of it.
Any ideas, anyone? This is kind of driving me mad, lol.

Connect a voltmeter - red lead to battery positive and black lead to coil positive ( should read no more than 0.5v) what is the voltage with

the ignition on

when cranking when it won't start

when cranking when it does start

You can then connect the red lead from the voltmeter to the negative side of the battery and the black lead to the common ground (black/yellow) wherever is easiest then complete the same three tests above - you should have no more than approx 0.3v
I suspect the effect of disconnecting other components has been more about disturbing the wiring than a direct electrical effect on the circuit

Ok, ran these checks suggested by Wookie58 this morning

Positive - Positive Voltage checks:
Ignition on: .33V
Cranking: 1.5V
Couldn't get it to start: NA

Negative - Negative
Ignition on: 0V
Cranking: 0V
Couldn't get it to start: NA
 
In the afternoon did some more troubleshooting with the  leads + battery to -coil positive, as I'm tugging around on some wires I see the voltage slowly drop to around 11V, shortly followed by the "Headlight Failure Indicator" lamp go off (lamp is normally lit with the headlight removed as in my case). Thought I blew a fuse, didn't know what was going on. Turned the key off/on a couple times, nothing. Unhooked the battery for an inspection of the 6-pin Ignition switch connector. A couple of the pins had some mild corrosion (aha moment), cleaned all the connections, sprayed with contact cleaner and reconnected the 6-pin connector. Hook the battery back, turned on the key, back in business. Gave the start button a push, cranked for about 5 seconds and fired up. Ran it for a few minutes, shut it off, restarted fine. Repeated this several times so keeping fingers crossed that I found the gremlin.
Might go back tomorrow with a follow-up of the + to - test to see if the 1.5V drop is gone, ran out of time today, other commitments. Hopefully it start and I get check that reading also.
Making progress

Good work, anything over 0.5v shows a resistance, this is only evident under load so a check on a dead circuit with an ohmmeter would not have shown a problem. Resistance diagnose with voltage drop has been the industry standard technique for a long time now and is what we teach dealership technicians. The reason these faults can be hard to track down on old bikes is the ign feed runs through so many connectors and switches that a small corrosion resistance at each point adds up to a problem when you add them all together. This is why many people fit a by-pass relay folk the coil feed but you need to be careful with electronic ignition. If you want to know how let me know 

05/12/2022 Update - After my last update I was making progress but the following day found it very difficult to get the bike to run so dug deeper looking for a wiring issue on the positive side wiring. After getting it to finally run was wiggling around on the plug wires while tweaking the throttle and got a small shock from the throttle housing, another ah hah moment. After disassembling the throttle control assembly I found one of the red wires with a small break in the insulation faintly exposing a strand or two of wire. Did a tiny repair with some clear fingernail polish to seal it, reinstalled the unit. She now starts somewhat difficult when cold but oddly still doesn't run quite right. Once warmed up a bit it will then start as expected but wants to only run/idle at near full choke, mind you I'm doing my testing with air-box off. I did throw some pods on it that I had from another old bike I use to have, still acts about the same, a tinge better. It will run at 6-7 grand fairly strong, didn't rev above that but then misfires and wants to die before settling in on idle.
Now when running "Wookie58's" voltage check on the positive side I am getting .06V with ignition on, cranking and running is now at approx. .75V -.9V still not within the .5V that is suggested. Note: Before fixing the throttle control short the voltage drop was between 2.5 and 4V when I could get it to run. Since then I've checked about everything I can think of electrically I can't seem to find anymore. In addition I installed new plug wires, cleaned the plugs, etc. so I assume it's time to go back into the carbs. Part of me still thinks electrical, what do you guys think? Maybe the coils, don't they usually act up when getting hot? The almost full choke to run half way decent indicates clogged pilot jets but they were clean on the previous carb check. One of the CV slide diaphragms has tiny hairline crack/tear approx. maybe a 3mm in length that I have to resolve, due to being tiny I don't think it would cause the major issue going on.
I really don't want to reinstall all the electrical accessory items, air-box, etc, and the works due to it being a pain to start when it's cold. I know if I put everything back together for a test ride it will probably throw a fit and not want to start.  I usually have to tease it with starting fluid and kind of baby it to life, after which it will start normal once warmed up. This has been a real hair puller for me. At any rate making a little more progress   
I'll attach a photo of the throttle housing wiring issue I fixed and try to upload a video of it running.

Here is a link to a video of the bike running that you can download\
www.dropbox.com/s/o8s0mobue8efvc9/KZ750.MOV?dl=0

Disconnect the coil feed and run a wire from the battery positive terminal with a 10a fuse in it directly to the coil DON'T LEAVE IT ON MORE THAN A COUPLE OF MINUTES WITHOUT THE ENGINE RUNNING if the problem is cured then your fault is definitely in the electrical supply to the ignition - if you look at my post on by-pass relay's there is a diagram of how to make this by-pass a permanent solution

05/17/2022 Update - Finally got around to performing Wookie's direct feed to the coil(s) test. With being wired direct I'm getting approx. .6V when cranking and when running is between 1 and 1.4V quite and improvement over running through the ignition. Oddly, it didn't seem to help it as far as starting and running compared to the 2.5 - 4V through the ignition. Pulled the carburetors for another breakdown and inspection. One of the carburetors had a film type gel blocking the tiny port of it's pilot jet. Cleaned and reassembled, running better but wild throttle swings. After a little more investigation with some contact cleaner found two of the carb boots leaking badly where they mate to the flat surface of the cylinder head. For those that are new to this, spraying contact cleaner, starting fluid, etc. around a suspected air leak will make an engine rev like crazy. Ordered a set of aftermarket boots through ebay from China so now back to the parts waiting to come in saga. Ever notice when your working on an old bike just about the time your ready for reassembly there's another gotcha around the corner where you have to wait for another part to come in. 
Anybody have any experience with these boots: item 282802816993 (paste this number into ebay search box)
@Wookie58 - Would you consider the 1-1.4V something to live with?  If not does this indicate a problem with the coils or some sort of back-feed even though wired direct? I'm pretty sure she going to run OK with the new carb boots as it now starts like it should when warmed up. Still a little iffy when cold but with leaking carb boots it makes sense as to why it would be difficult to start when cold.
 

You might want to read Elfarms experiences with cheap boots
  KZ750 CV34 wants to rev to 4.5k? - Page 2 - KZRider Forum - KZRider, KZ, Z1 & Z Motorcycle Enthusiast's Forum

Ref the electrics -
Is the red/yellow disconnected from the coils ?
Are these voltage readings from the temp by-pass wire ?
If the answer to both of the above is yes then with your meter connected from battery positive to new coil feed should read minimal voltage as long as you are using at least 20g cable (see the below calculator for expected volt drop)
What method have you used to connect the temp by-pass ?
The voltage reading should be the same regardless of whether it is cranking or running as you are simply measuring the voltage difference at each end of the by-pass wire. The main issue with volt drop due to resistance is that resistance causes heat and heat increases resistance so the longer it has current running through the greater the resistance will be until it stops working altogether. Then after it has been switched off and had time to cool down the whole cycle starts again (ever heard somebody say they break down every half an hour ?)
 

If you’re really trying to fix the bike up, go ahead and start to eliminate variables. Non-leaking boots will remove that variable from your equation on why the bike acts like it does. I will say, to my own experience, if you have the money for the carb boots, just go ahead and buy OEM and you won’t have to screw around with them to get them to work properly. Yes it’s a pretty penny, but it’s higher manufacturing quality. It’s a get what you pay for type situation. 

@Wookie58
Is the red/yellow disconnected from the coils? Yes
Are these voltage readings from the temp by-pass wire? Yes
Using at least 20g cable? Yes, using 18g
What method have you used to connect the temp by-pass?
The temporary bypass method I used followed your guidelines, consists of an inline 5A fuse (what I had on hand) running to a soldered and heat-shrinked branch connection so that each coil is fed directly. The other end is hooked directly to the positive battery terminal. The multimeter connection -negative lead is connected to the RS coil +positive terminal and the positive meter lead to the positive battery connection. All together approx. 4ft. of wire is used.

Ok so you have fallen in a classic trap and sent yourself down a rabbit hole   the way a fuse works is that when a current greater than it's rating is passed through it starts to heat up then blows (during the heating process the resistance increases) by using a 5 amp fuse you have built your own fault into the equation. Calculating parallel resistances involves a formula so I have put the calculations below, as you can see at any point when both coils are energised you are exceeding the current rating of the fuse (significantly when the voltage is higher with the engine running which is why you have a greater volt drop with the engine running due to the higher current draw and heat build up)
As a rule of thumb to calculate a fuse rating you should take the maximum current flow, add 10% then select the first available fuse greater than that value. In this case 
8.94 amps + 10% = 9.83 amps so you would select a 10 amp fuse as a minimum (I would recommend a 15 amp fuse in this case to allow for spikes if this wasn't a temp set up)